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On Mono- and Epimorphisms in Varieties of Ordered Algebras |
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| Authors: | Valdis Laan Sohail Nasir |
| Institution: | 1. Institute of Mathematics, Faculty of Mathematics and Computer Science , University of Tartu , Tartu , Estonia vlaan@ut.ee;3. Institute of Mathematics, Faculty of Mathematics and Computer Science , University of Tartu , Tartu , Estonia |
| Abstract: | We study morphisms in varieties of ordered universal algebras. We prove that (i) monomorphisms are precisely the injective homomorphisms and that (ii) every regular monomorphism is an order embedding, but the converse is not true in general. We also give a necessary and sufficient condition for a morphism to be a regular epimorphism. Finally, we discuss factorizations in such varieties. |
| Keywords: | Directed kernel Extremal epimorphism Extremal monomorphism Factorization Ordered algebra Order-congruence Regular epimorphism Regular monomorphism |